Adaptation of Parameters in a Communication Network

ABSTRACT

A distributed parameter update procedure is provided for updating parameters that do not have discrete values. When a parameter value is changed, a search is conducted of a parameter space to find a new parameter value minimizes some cost function. The cost function is derived based on the current parameter settings in neighboring nodes. The distributed parameter update procedure may simplify the search process by localizing the search of the parameter space for a new parameter value to the vicinity of the current parameter setting. In some embodiments, the search is conducted along a line of steepest descent emanating from the current parameter setting.

BACKGROUND

The present invention relates generally to the configuration of acellular communication network and, more particularly, to a method ofself-configuration of parameter settings for a cellular communicationnetwork.

In a mobile communication network, the coverage area of the network isdivided into a plurality of cells. Conventionally, the configuration ofcells and the assignment of certain parameters are set during cellplanning and remain static once the system is deployed. As an example,frequencies may need to be assigned to the cells in a manner to reduceinterference between cells. This requirement usually means that the samefrequency is not reused in neighboring cells. As another example, thecells may be assigned locally unique reference signals (RSs), which areused by the mobile terminal to identify the cells and synchronize to thenetwork.

The assumption that the network topology will remain static once asystem is deployed is no longer true. It is now common for cells to beadded or subtracted from a network after the system is deployed. Forexample, pico cells or other low power cells may be deployed in someareas of the network in order to improve coverage. Also, home basestations may be deployed in areas where network coverage is alreadyprovided. As new cells are added or subtracted, a different set ofneighbor cell relationships is created.

Some mechanism is needed in order to prevent parameter conflicts betweenneighboring cells when new cells are deployed. For example, a new cellshould not be assigned frequencies or RS patterns that conflict withexisting assignments. Conventionally, the network administrator canmanually assign parameters to the new cells in order to avoid conflicts.However, this is becoming increasingly more difficult as the number ofcells in the network increases. In some cases, the network administratormust reconfigure existing cells in order to avoid conflicts. The cellplanning that precedes the deployment of new cells can therefore becostly and time-consuming.

One way to simplify deployment of new cells is to make the networkself-configuring in as many aspects as possible. U.S. patent applicationSer. No. 13/072,496 filed Mar. 25, 2011 which is incorporated byreference herein in its entirety, discloses a general framework forupdating system parameters when new cells are deployed. This patentapplication describes a distributed parameter update procedure based onthe exchange of impact functions between neighboring cells. An impactfunction is a function describing how changes in a parameter setting ofa first cell will affect a neighboring cell. When a parameter setting isupdated by a cell, the cell exchanges impact functions with itsneighboring cells. After the exchange of impact functions, the updatingcell can compute a new parameter setting that minimizes the cumulativeimpact on its neighboring cells. A similar technique is used in othercells, so that as a whole the system gradually converges to an optimumor near optimum result.

The technique described above can be applied to a wide range of systemparameters. In cases where the parameter setting is limited to a finitenumber of discrete values, the impact function can be easily tabulatedand exchanged among cells. For a continuous parameter, such as transmitpower, the same formulation can be used only if the parameter isquantized. If the quantization step is too large, quantization error maylead to performance degradation. If the quantization step is too small,the large amount of data to be exchanged among cells may exceed thecapacity of the inter-cell connection or incur excessive delay.

Accordingly, there remains a need for a distributed parameter updateprocedure for updating parameters that can have continuous values.

SUMMARY

Particular embodiments of the present invention provide methods andapparatus for updating, in a distributed manner, parameters of a networknode that can have a continuous (non-discrete) value. When a parametervalue is changed, a search is conducted of a parameter space to find anew parameter value that minimizes some cost function. The cost functionis derived based on the current parameter settings in neighboring nodes.Certain embodiments of the present invention simplify the search processby localizing the search of the parameter space for a new parametervalue to the vicinity of the current parameter setting. In someembodiments, the search is conducted along a line of steepest descentemanating from the current parameter setting.

Exemplary embodiments of the invention comprise a distributed parameterupdate method implemented by a network node in a mobile communicationnetwork. The method may be performed iteratively by the network node. Inone exemplary method, a network node receives current parameter settingsfor each of one or more neighboring nodes in its local network. Thecurrent parameter settings may comprise settings computed in theprevious iteration of the process. The network node then computes agradient of a summed cost function for network node. The summed costfunction is a function of the current parameter settings for the networknode and the neighboring nodes in its local network. The network nodethen determines a revised parameter setting by searching the parameterspace along the gradient of the summed cost function for a solution thatminimizes the summed cost function. Once the new parameter value isdetermined, the network node sends its new parameter setting to theneighboring nodes in its local network. After exchanging new parametersettings with its neighbor nodes, the process may be repeated.

In another exemplary embodiment, the network node receives currentparameter settings for each of one or more neighboring nodes in itslocal network. After receiving the current parameter settings, thenetwork node determines a summed cost function as a function of thecurrent parameter settings for network node and its neighboring nodesThe network node then computes a gradient of the summed cost functionfor the network node. The network node then determines a revisedparameter setting by searching the parameter space along the gradient ofthe summed cost function for a solution that minimizes the summed costfunction. Once the new parameter value is determined, the network nodesends its new parameter setting to the neighboring nodes in its localnetwork. After exchanging new parameter settings with its neighbornodes, the process may be repeated.

In another exemplary embodiment, the network node exchanges currentparameter settings with the neighboring nodes in a local network of thenetwork node. The network node then computes a partial derivative of alocal cost function with respect to each of its neighboring nodes. Aseparate instance of the local cost function is computed for eachneighboring node. Once the partial derivatives are computed, they areexchanged with the neighboring nodes. The network node then computes agradient of a summed cost function at its current parameter settingbased on the partial derivatives received from its neighboring nodes.The computed gradient is exchanged with the neighboring nodes. In theexchange, the network node receives gradients computed by each of itsneighboring nodes. After this exchange, the network node computes alocal impact function based on the gradients. A separate instance of thelocal impact function is computed for each of the neighboring nodes. Thenetwork node exchanges the local impacts functions with its neighboringnodes. After the exchange, the network node computes a summed impactfunction as a weighted sum of the impact functions of the network nodeand its neighboring nodes. The network node determines a new parametersetting based on the summed impact function and the gradient of thesummed cost function. The new parameter value for the network node isthen sent to the neighboring nodes. After exchanging new parametersettings with its neighbor nodes, the process may be repeated.

Other embodiments of the invention comprise a network node configured toimplement the distributed parameter update procedures described above.In one embodiment, the network node comprises an interface circuit forcommunicating with one or more neighboring nodes in a local network ofthe network node, and a configuration processor for determining aparameter setting for the network node. The configuration processor isconfigured to implement the methods described as described in paragraphs[009]-[011].

Certain embodiments of the present invention enable the use of adistributed parameter update procedure for parameters that can have acontinuous value. The use of local impact functions in some embodimentsrequires the exchange of less information between network nodes ascompared to a full description of the cost functions. Thus, bandwidth isconserved and latency is reduced. Further, the search of the parameterspace is restricted to a line extending from the current parametersetting requires fewer processing resources.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an exemplary communication network implementing adistributed parameter update procedure.

FIG. 2 illustrates a first exemplary distributed parameter updateprocedure.

FIG. 3 illustrates a second exemplary distributed parameter updateprocedure for updating parameters.

FIG. 4 illustrates a third exemplary distributed parameter updateprocedure for updating parameters.

FIG. 5 illustrates a fourth exemplary distributed parameter updateprocedure for updating parameters.

FIG. 6 illustrates an exemplary network node in the communicationnetwork.

DETAILED DESCRIPTION

Referring now to the drawings, FIG. 1 illustrates a cellularcommunication network 10 implementing a distributed parameter updateprocedure. The geographic area covered by the communication network 10is divided into a plurality of cells 12. Each cell corresponds to a node20. The nodes 20 may comprise base stations that provide service to userterminals 30 in their respective cells 12. In some instances, the nodes20 may comprise user terminals 30 capable of peer-to-peercommunications. For convenience, the cells 12 are shown as being ofequal size and being arranged in a hexagonal pattern. Those skilled inthe art will appreciate, however, that the size of the cells 12 may varyand that the coverage area of the cells 12 may overlap.

In the communication network 10, the nodes 20 may need to adapt aparameter, such as transmit power, responsive to short-term changes inthe communication network 10. The parameter setting in each cell 12 willaffect neighboring cells. For example, if a node 20 transmits at highpower, it creates interference in the neighboring cells 12, whichdecreases capacity in the neighboring cells 12. On the other hand, ifthe node 20 transmits at a low power, it may be operating at less thanmaximum capacity. It should be noted that transmit power is a parameterthat can have a continuous value between a minimum value (e.g., 0) and amaximum value.

A distributed parameter update procedure is used to coordinate theparameter settings between cells 12 in order to optimize some aspect ofnetwork performance. For example, the distributed parameter updateprocedure could be used to determine transmit power settings for thenodes 20 to maximize system capacity. The distributed parameter updateprocedure uses impact functions that describe how parameter settings inone cell 12 affects its neighboring cells 12. In the parameter updateprocedure, each node 20 computes a set of impact functions thatdescribes how the parameter settings in neighboring cells 12 affects itsown cell 12 and exchanges the impact functions with its neighboringcells 12. The node 20 in each cell 12 uses the impact functions receivedfrom nodes 20 in neighboring cells 12 to determine its own parametersetting.

FIG. 2 illustrates a distributed parameter update procedure 50. Thedistributed parameter update procedure 50 is an iterative process thatbegins with the updating of a parameter by each node 20 based on thecurrent parameter settings and cost functions exchanged between thenodes 20 (block 55). After updating the parameter, the nodes 20 exchangethe updated parameter settings (block 60).

The distributed update procedure 50 applies in a straightforward way toparameters that have a finite set of discrete values. However,application of the distributed parameter update procedure to parametersthat can have a continuous value is more difficult. Examples ofcontinuous value parameters include the transmit power of a node 20 andantenna weights for nodes 20 in a multiple-input, multiple output (MIMO)system with multiple antennas. One of the problems in applying thedistributed parameter update procedure to such parameters is theexchange of cost functions. For continuous variables, the amount ofinformation needed to fully describe the cost function makes theexchange of information costly in terms of bandwidth and latency.Another problem is that the parameter space is quite large. Performing afull search of the parameter space for an optimum solution would betime-consuming and would require significant processing resources.

In one or more embodiments of the present invention, a node 20 restrictsits search of the parameter space to a one dimensional subspace in thevicinity of the current parameter setting. In one exemplary embodiment,a node 20 searches the parameter space along a line of steepest descentemanating from the current parameter setting. This approach reduces theamount of information required to describe the behavior of the costfunction in the vicinity of the current parameter setting, and requiresless information to describe than the full cost function. Therefore, itis possible to apply the distributed parameter update technique tovariables that have continuous values.

Introducing the notation used in the remainder of this description, eachcell 12 in the communication network 10 is identified by a unique indexi, and a one-to-one correspondence between nodes 20 and cells 12 isassumed. At a given time instant n, a parameter vector p_(i) associatedwith node i can be set by the node to adapt to changes in thesurrounding environment. If the parameter is the transmit antennaweights in a MIMO system, it can be set to any complex number. If theparameter is the transmit power of a node 20, it can be set to anynon-negative number. By convention, variables are denoted by bold facetype and the values it takes by normal lower case letters, such as p_(i)^(n), where the superscript n indicates the time index.

Each node i has a list of neighboring nodes determined by a proximitymeasure such as distance or intensity of radio interference. Thedetermination of the neighboring nodes is not a material aspect of theinvention, and techniques for determining neighbor sets are well-knownin the art. In general, the neighbor set is determined based on receivedsignal measurements. Nodes whose signal strength measurements exceed athreshold are included in the neighbor set. The set of neighboring nodesof node i is denoted

_(i). It is assumed that the neighbor relationship is reciprocal, i.e.,jε

_(i) if and only if iε

_(j). The union of the neighbor set

_(i), with node i is referred to as the local network with respect tonode i and is denoted

_(i).

Each node if can communicate with its neighboring nodes in

_(i) to exchange parametric information required to evaluate a costfunction defined for its local network

_(i). The cost function is given by

(ip _(j) |ε

_(i))=

(p _(i) ,p _(j) |jε

_(i))  Eq. (1)

After exchanging information with its neighboring nodes, each node icomputes a new parameter value that minimizes a summed cost functiongiven by:

$\begin{matrix}{p_{i}^{n + 1} = {\underset{p_{i}}{\arg \; \min}{\sum\limits_{j \in _{i}}{w_{j}{C_{_{j}}\left( {{\left. p_{i} \middle| p_{k} \right. = p_{k}^{n}},{\forall{k \in {_{j} - \left\{ i \right\}}}}} \right)}}}}} & {{Eq}.\mspace{14mu} (2)}\end{matrix}$

That is, each node i searches the parameter space and selects itsparameter value as the one that minimizes the weighted sum of the costfunctions corresponding to the local networks of the nodes in

_(i) (the local network of the central node i), assuming all otherparameters remain the same as previously communicated at time instant n.The updated parameter value is then communicated to the neighboringnodes while at the same time the updated parameter values of neighboringnodes are also received.

For continuous parameters, such as transmit power, a search over theentire parameter space for the optimum solution of p_(i) would becomputationally complex and time-consuming. Instead of searching overthe entire parameter space for a globally optimum solution of p_(i) asdescribed above, a simplified search may be implemented wherein thesearch of the parameter space is made in each iteration along thedirection of the steepest descent. This approach restricts theoptimization problem to a local one that is easier to define and thusmore efficiently communicated between neighboring nodes.

FIG. 3 illustrates a generalized distributed update procedure 100implemented by the network nodes 20 according to embodiments of theinvention. The distributed parameter update procedure 100 is aninteractive process. Network node i receives current parameter settingsfor each of one or more neighboring nodes in its local network

_(i) (block 110). The current parameter settings are those computed inthe previous iteration. Network node i then computes a gradient of asummed cost function C_(i) ^(n)(p_(i)) for network node i (block 120).The summed cost function C_(i) ^(n)(p_(i)) is a function of the currentparameter settings for network node i and the neighboring nodes

_(i) in its local network

_(i). Network node i then determines a revised parameter setting bysearching the parameter space along the gradient of the summed costfunction for the solution that minimizes the summed cost function (block130). Once the new parameter value is determined, the network node isends its new parameter setting to the neighboring nodes

_(i) in its local network

_(i) (block 140). After exchanging new parameter settings with itsneighbor nodes

_(i), the process is repeated.

In a first exemplary embodiment, the summed cost function given in Eq.(2) is rewritten as:

$\begin{matrix}{{C_{i}^{n}\left( p_{i} \right)} = {\sum\limits_{j \in _{i}}{w_{j}{C_{_{j}}\left( {{\left. p_{j} \middle| p_{k} \right. = p_{k}^{n}},{\forall{k \in {_{j} - \left\{ i \right\}}}}} \right)}}}} & {{Eq}.\mspace{14mu} (3)}\end{matrix}$

The dependence on the neighbor nodes' parameter is dropped to highlightthe fact that the cost function is a function of its own parametervariable p_(i). By convention, the parameter p_(i) is a column vector ifit consists of more than one variable. The gradient of the cost functionin Eq. (2) is a row vector given by:

$\begin{matrix}{{{\nabla{C_{i}^{n}\left( p_{i} \right)}} \equiv \frac{\partial{C_{i}^{n}\left( p_{i} \right)}}{\partial p_{i}}} = \begin{bmatrix}\frac{\partial{C_{i}^{n}\left( p_{i} \right)}}{\partial p_{i,1}} & \frac{\partial{C_{i}^{n}\left( p_{i} \right)}}{\partial p_{i,2}} & \ldots\end{bmatrix}} & {{Eq}.\mspace{14mu} (4)}\end{matrix}$

The elements of Eq. (4) are partial derivatives of the summed costfunction with respect to the corresponding variables in the parametervector. The gradient evaluated at p_(i) ^(n) is

$\begin{matrix}{\left( \gamma_{i}^{n} \right)^{T} = \left. {{\nabla{C_{i}^{n}\left( p_{i}^{n} \right)}} \equiv {\frac{\partial}{\partial p_{i}}{C_{i}^{n}\left( p_{i} \right)}}} \right|_{p_{i} = p_{i}^{n}}} & {{Eq}.\mspace{14mu} (5)}\end{matrix}$

where ( )^(T) is the vector (or matrix) transpose. Therefore, thegradient γ_(i) ^(n) is a column vector with the same dimension as theparameter p_(i).

In this embodiment, it is presumed that the cost function is known andthat the gradient of the cost function can be evaluated at the currentparameter value. The distributed parameter update procedure updates theparameter value by searching for a better solution than the current onealong the direction of a line segment defined by p_(i) ^(n)−γ_(i) ^(n)α,where α is a nonnegative scalar. The scalar a that may be upper boundedby the constraints of the problem. In other words, the network node iseeks the a value that minimizes the cost function:

$\begin{matrix}{\overset{\sim}{\alpha} = {\underset{\alpha}{\arg \; \min}{C_{i}^{n}\left( {p_{i}^{n} - {\gamma_{i}^{n}\alpha}} \right)}}} & {{Eq}.\mspace{14mu} (6)}\end{matrix}$

The network node i then computes the new parameter value according to:

p _(i) ^(n+1) =p _(i) ^(n)−γ_(i) ^(n){tilde over (α)}  Eq. (7)

The updated parameter values are then exchanged among neighboring nodesbefore the next iteration cycle starts.

FIG. 4 illustrates a method 200 of determining a parameter setting inthe situation where the cost functions for the neighboring nodes

_(i) are known or can be determined. Network node i receives currentparameter settings for each of one or more neighboring nodes

_(i) in its local network

_(i) (block 210). After receiving the current parameter settings,network node i determines a summed cost function according to Eq. (3)given the current parameter settings (block 220). Network node i thencomputes a gradient of the summed cost function C_(i) ^(n)(p_(i)) fornetwork node i (block 230). The gradient may be computed according toEq. (5). Network node i then determines a revised parameter setting bysearching the parameter space along the gradient of the summed costfunction for the solution that minimizes the summed cost function (block240). Once the new parameter value is determined, the network node isends its new parameter setting to the neighboring nodes

_(i) in its local network

_(i) (block 250).

In many cases, each parameter p_(i) is also constrained to be in afeasible set S_(i). In this case, a function projecting the perturbedparameter value onto S_(i) may be used. In cases where the parametervalue is limited to a predefined set, the parameter is given by:

p _(i) ^(n+1) =Q _(S) _(i) (p _(i) ^(n)−γ_(i) ^(n){tilde over (α)})  Eq.(8)

where Q_(S) _(i) denotes a projection function onto the set S_(i). Forexample, when p_(i) represents the transmit power of node i, S_(i)=[0,P_(max,i)] represents the interval of feasible power levels of node i,where P_(max,j) denotes the maximum transmit power level of node i. Inone embodiment, the projection function Q_(S) _(i) is given by:

$\begin{matrix}{{Q_{S_{i}}(x)} = {{\left\lbrack {P_{\max,i} - \left\lbrack {P_{\max,i} - x} \right\rbrack^{+}} \right\rbrack^{+}.{where}}\text{:}}} & {{Eq}.\mspace{14mu} (9)} \\{\lbrack x\rbrack^{+} = \left\{ {\begin{matrix}x & {{{if}\mspace{14mu} x} \geq 0} \\0 & {{{if}\mspace{14mu} x} < 0}\end{matrix}.} \right.} & {{Eq}.\mspace{14mu} (10)}\end{matrix}$

The evaluation of the summed cost function given in Eq. (3) requiresknowledge of the individual cost functions

_(A) _(j) for all nodes jε

_(i). If this information is not available at node i, it needs to becommunicated from the neighboring nodes

_(i). This exchange may be too costly in terms of bandwidth or latencyif the cost functions are very complicated, or if the cost functions donot have a functional form (i.e., cannot be represented by an Eq.).Moreover, the cost function may change as network topology orpropagation environment evolves over time, making the exchange of localcost functions even more inefficient.

Fortunately, the steepest descent approach requires only knowledge ofthe cost function along the line of gradient in the neighborhood of thecurrent parameter values. This restricted function of a single variable,referred to herein as the “local cost function,” is easier to describethan the functional form of the cost function. Therefore, in a secondembodiment of the invention, each network node i exchanges informationdescribing its local cost function in the vicinity of its currentparameter setting with its neighboring nodes.

In the second embodiment, each node i first computes the partialderivative g_(j→i) ^(n+1) of its local cost function for each of itsneighboring nodes. The partial derivative may be computed according to:

$\begin{matrix}{g_{j\rightarrow i}^{n + 1} = \left. {\frac{\partial}{\partial p_{j}}{C_{_{i}}\left( {{\left. p_{j} \middle| p_{k} \right. = p_{k}^{n}},{\forall{k \in {_{i} - \left\{ j \right\}}}}} \right)}} \right|_{p_{j} = p_{j}^{n}}} & {{Eq}.\mspace{14mu} (11)}\end{matrix}$

After exchanging the partial derivatives, each node i will havesufficient information to compute its search direction. The searchdirection can be computed according to:

$\begin{matrix}{\gamma_{i}^{n + 1} = {\sum\limits_{j \in _{i}}{w_{j}g_{i\rightarrow j}^{n + 1}}}} & {{Eq}.\mspace{14mu} (12)}\end{matrix}$

Once the search direction is determined, it is then communicated to theneighboring nodes

_(i). That is, each node i exchanges the computed search directioncomputed in Eq. (12) with each of its neighboring nodes

_(i). The exchanged search direction information is used at each node ito determine a local impact function for each of its neighboring nodes

_(i). In one embodiment, the local impact function is computed accordingto:

I _(j→i) ^(n+1)(α)=

(p _(j) ^(n)−γ_(j) ^(n+1) α|p _(k) =p _(k) ^(n) ,∀kε

_(i) −{j})  Eq. (13)

This local impact function describes the contribution of the parameterset by each neighboring node

_(i) to the summed cost function

of node i. Since it is a scalar function of a single variable α, it canbe more concisely represented than the local cost function itself. Aseparate instance of the local impact function is computed for eachneighboring node

_(i).

After exchanging the local impact functions with it neighboring nodes

_(i), the network node i can compute a summed impact function describinghow changes to its own parameter setting will impact its neighboringnodes

_(i). The network node i seeks the α value that minimizes the followingsummed impact function:

$\begin{matrix}{\overset{\sim}{\alpha} = {\underset{\alpha}{\arg \; \min}{\sum\limits_{j \in _{i}}{w_{j}{I_{i\rightarrow j}^{n + 1}(\alpha)}}}}} & {{Eq}.\mspace{14mu} (14)}\end{matrix}$

The network node i then computes the new parameter value according to:

p _(i) ^(n+1) =p _(i) ^(n)−γ_(i) ^(n+1){tilde over (α)}.  Eq. (15)

The updated parameter values are then exchanged among neighboring nodesand the next iteration of the distributed parameter update and theprocess is repeated using the new parameter settings.

FIG. 5 illustrates a method 300 of determining a parameter setting inthe situation where the cost functions for the neighboring nodes

_(i) are not known. Network node i exchanges current parameter settingswith the neighboring nodes

_(i) in a local network

_(i) (block 305). The network node i then computes a partial derivativeof a local cost function

with respect to each of its neighboring nodes (block 310). The partialderivative may be computed according to Eq. (11). A separate instance ofthe local cost function

is computed for each neighboring node

_(i). Once the partial derivatives are computed, they are exchanged withthe neighboring nodes

_(i) (block 315). The network node i then computes a gradient of asummed cost function at its current parameter setting based on thepartial derivatives received from its neighboring nodes

_(i) (block 320). The gradient may be computed according to Eq. (12).The computed gradient is exchanged with the neighboring nodes (block325). In the exchange, node i receives gradients computed by each of itsneighboring nodes. After this exchange, the network node i computes alocal impact function according to Eq. (13) based on the gradients(block 330). A separate instance of the local impact function iscomputed for each of the neighboring nodes. The network node i exchangesthe local impacts functions with its neighboring nodes (block 335).After the exchange, the network node i possesses a local impact functiondescribing how changes in its parameter setting will affect each of itsneighboring nodes. The weighted sum of these impact functions yields asummed impact function of the variable α (block 340). The network node idetermines a new parameter setting based on the summed impact functionand the gradient of the summed cost function (block 345). Moreparticularly, the network node searches for the value of α thatminimizes the summed impact function and computes the new parametervalue according to Eq. (14) and Eq. (15). The new parameter value forthe network node is then sent to the neighboring nodes (block 350).

In the embodiment shown in FIG. 5, the way that the impact function isrepresented needs to be agreed upon before the information exchangetakes place. There may be several ways to represent the impact function.A straightforward solution is to sample the function and exchange the(possibly quantized) sample values. Alternatively, the function can beapproximated by its Taylor series expansion and the nodes 20 can thenexchange a selective number of significant coefficients. In any case,there may be a phase in the coordination process in which the formats ofthe impact functions are communicated and agreed upon. This phase canoccur as often or as infrequent as needed. With this setup/update phase,the subsequent exchanges of information among neighbor nodes may befurther reduced by passing only the search direction as opposed to theimpact function.

A practical example of a particular embodiment of the present inventionwill now be described to illustrate one possible use of the invention.Power control is a commonly encountered problem in a cellular network.If a node is transmitting at very high power, it may create too muchinterference to neighboring cells. If its transmit power is set too low,it may not be operating at its maximal potential. Ideally, a centralnode can be employed to coordinate the transmit power from the multiplecells so that the overall network-wise capacity is maximized whilemaintaining a certain minimal quality of service for the individualcells. In practice, however, such a central node may not be availableand a distributed solution is needed.

FIG. 1 illustrates a local network

_(i) centered on node P₀, which for purposes of this example is assumedto be a base station. The neighbor set

₀ for node P₀ includes nodes P₁, P₂, P₃, P₄, P₅, and P₆. A user terminalbeing served by node P₀ receives its desired signal with a power levelof p₀g₀₀, where p₀ is the transmit power of node P₀ and g₀₀ is the pathgain between node P₀ and the user terminal. In addition, it alsoreceives interference from at least the six cells 12 in its neighborlist at a level of p_(j)g_(0j), where p_(j) is the transmit power ofneighboring node j and g_(0j) is the path gain between neighboring nodej and the user terminal. Based on the information available to node P₀,the capacity of the user terminal it serves is given by:

$\begin{matrix}{R = {{\log\left( {1 + \frac{p_{0}g_{00}}{N_{0} + {\sum\limits_{j \in _{0}}{p_{j}g_{0j}}}}} \right)}\mspace{14mu} {nats}}} & {{Eq}.\mspace{14mu} (16)}\end{matrix}$

where N₀ is the noise variance.

The goal of the distributed parameter update method is to maximize thesummed capacity of all the cells 12 in the network 10 subject to a powerconstraint at each node and a certain minimal requirement constraint forthe individual cells 12. Such constraint can be, for example, a limit onthe highest interference each user terminal experiences. Theinterference may be expressed by the ratio:

$\begin{matrix}{\frac{p_{j}g_{0j}}{p_{0}g_{00}} < \lambda} & {{Eq}.\mspace{14mu} (17)}\end{matrix}$

The requirement is, therefore, to keep the ration given by Eq. (16)below a predetermined threshold λ for all nodes jε

₀.

The local cost function defined in Eq. (1) is chosen to be the negativeof the capacity and is given by:

$\begin{matrix}{{C_{_{0}}\left( p_{j} \middle| {j \in _{0}} \right)} = {{- R} = {\log\left( \frac{N_{0} + {\sum\limits_{j \in _{0}}{p_{j}g_{0j}}}}{N_{0} + {\sum\limits_{j \in _{0}}{p_{j}g_{0j}}}} \right)}}} & {{Eq}.\mspace{14mu} (18)}\end{matrix}$

The local cost functions for any jε

₀,

_(A) _(j) , can be similarly defined and the weighted and summed costfunction given in Eq. (2) can be evaluated subsequently.

The partial derivatives of Eq. (18) can be easily derived, and are givenby:

$\begin{matrix}{{{\frac{\partial}{\partial p_{0}}{C_{_{0}}\left( p_{j} \middle| {j \in _{0}} \right)}} = {{- \frac{g_{00}}{N_{0} + {\sum\limits_{j \in _{0}}{p_{j}g_{0j}}}}}\mspace{14mu} {and}}}{{\frac{\partial}{\partial p_{k}}{C_{_{0}}\left( p_{j} \middle| {j \in _{0}} \right)}} = \frac{p_{0}g_{00}g_{0k}}{\begin{matrix}\left( {N_{0} + {\sum\limits_{j \in _{0}}{p_{j}g_{0j}}}} \right) \\\left( {N_{0} + {\sum\limits_{j \in _{0}}{p_{j}g_{0j}}}} \right)\end{matrix}}}} & {{Eq}.\mspace{14mu} (19)}\end{matrix}$

for kε

₀, k≠0. With the local cost function defined and its partial derivativederived, the distributed parameter update procedures of FIG. 3, 4 or 5can be carried out.

In some embodiments of the invention, the constraint given by Eq. (17)on highest interference level, the summed cost function over the rangeof valid α in the line search given in Eq. (6) and Eq. (14) can beclosely approximated by a linear function, thereby further reducing theamount of information exchanged among neighboring nodes.

FIG. 6 illustrates the main functional elements of an exemplary node 20implementing the distributed parameter update method as hereindescribed. The node 20 is a base station in a cell 12 of thecommunication network 10. The node 20 comprises transceiver circuits 22,control circuits 24, and an interface circuit 30. The transceivercircuits 22 comprise one or more receivers and transmitters forwirelessly communicating over an air interface with user terminals inthe cell served by the node 20. The control circuit 24 includes aconfiguration processor 26 to determine a parameter setting for the node20, and memory 28 for storing program instructions and data needed foroperation. The configuration processor 26 may comprise one or moremicroprocessors, hardware, firmware, or a combination thereof. Memory 28may comprise non-volatile memory, such as read-only memory. Theinterface circuits 30 are configured to connect with a signaling networkand enable the exchange of cost functions and parameter settings withother nodes 20.

The disclosed embodiments of the present invention enable the use of adistributed parameter update procedure for parameters that can have acontinuous value. The use of local impact functions in some embodimentsrequires the exchange of less information between network nodes ascompared to a full description of the cost functions. Thus, bandwidth isconserved and latency is reduced. Further, the search of the parameterspace is restricted to a line extending from the current parametersetting, requires fewer processing resources.

The present invention may be carried out in other ways than thosespecifically set forth herein without departing from essentialcharacteristics of the invention. The disclosed embodiments are thus tobe considered in all respects as illustrative and not restrictive, andall changes coming within the meaning and equivalency range of theappended claims are intended to be embraced therein.

What is claimed is:
 1. A method of determining parameter settings for anetwork node in a communication network, the method comprising:receiving, at a network node, current parameter settings for each of oneor more neighboring nodes in a local network of the network node;computing a gradient of a summed cost function for the network node as afunction of the current parameter settings for the network node and itsneighboring nodes; determining a revised parameter setting for thenetwork node by searching a parameter space along the gradient of thesummed cost function; and sending the revised parameter setting for thenetwork node to the neighboring nodes.
 2. The method of claim 1 whereincomputing a gradient of a summed cost function comprises: receiving apartial derivative with respect to the network node of a local costfunction for each of one or more of the neighboring nodes; and computingthe gradient of a summed cost function for the network node based on thereceived partial derivatives of the local cost functions for theneighboring nodes.
 3. The method of claim 2 wherein receiving a partialderivative with respect to the network node of a local cost function foreach of one or more of the neighboring nodes comprises: exchangingcurrent parameter settings with the neighboring nodes, wherein thenetwork node receives current parameter settings for its neighboringnodes during the exchange; computing, at the network node, a partialderivative of a local cost function for the network node based on thecurrent parameter settings of the neighboring nodes; and exchanging thepartial derivatives computed by the network node with correspondingpartial derivatives computed by the neighboring nodes based on thecurrent parameter settings.
 4. The method of claim 1 wherein determininga revised parameter setting for the network node comprises: receiving alocal impact function for each of one or more of the neighboring nodes,wherein the local impact function from each neighboring node indicates acontribution of the parameter setting by the network node on a summedcost function for the neighboring node; determining a summed impactfunction for the network node based on the local impact functions forthe neighboring nodes and a local impact function for the network node;and determining the revised parameter setting based on the summed impactfunction and the gradient of the summed cost function.
 5. The method ofclaim 4 wherein receiving a local impact function for each of one ormore of the neighboring nodes comprises: exchanging, with theneighboring nodes, the gradient of the summed cost function for thenetwork node for corresponding gradients of the summed cost functionsfor the neighboring nodes; computing a set of local impact functions forthe network node and the neighboring nodes based on the exchangedgradients of the summed cost functions; and exchanging, the local impactfunction computed by the network node for corresponding local impactfunctions computed by the neighboring nodes.
 6. The method of claim 4wherein determining a summed impact function for the network nodecomprises determining a weighted sum of the local impact functions forthe neighboring nodes and the local impact function for the networknode.
 7. The method of claim 4 wherein determining the revised parametersetting based on the summed impact function and the gradient of thesummed cost function comprises: determining a scalar that minimizes thesummed impact function; and computing the revised parameter setting forthe network node as a function of the scalar and the gradient of thesummed cost function for the network node.
 8. The method of claim 1further comprising: receiving, at the network node, current parametersettings for each of one or more of the neighboring nodes; anddetermining the summed cost function for the network node based on thecurrent parameter settings of the neighboring nodes.
 9. The method ofclaim 8 wherein computing a gradient of a summed cost function for thenetwork node at a current parameter setting for the network nodecomprises: determining a partial derivative of the summed cost functionwith respect to each of one or more variables in the parameter setting;and computing the gradient of the summed cost function for the networknode as a function of the partial derivatives.
 10. The method of claim 8wherein determining a revised parameter setting for the network nodecomprises: searching the parameter space along the gradient of thesummed cost function to find a scalar that minimizes the summed costfunction; and computing the new parameter setting as a function of thegradient and the scalar.
 11. The method of claim 1 wherein determining arevised parameter setting for the network node further comprisesconstraining the revised parameter setting to be a member of apredetermined set of parameter settings.
 12. A method of determiningparameter settings for a network node in a communication network, themethod comprising: receiving, at a network node, current parametersettings for each of one or more neighboring nodes in a local network ofthe network node; determining a summed cost function for the networknode based on the current parameter settings of the network node and theneighboring nodes; computing a gradient of the summed cost function at acurrent parameter setting for the network node; determining a revisedparameter setting for the network node by searching a parameter spacealong the gradient of the summed cost function; and sending the revisedparameter setting for the network node to the neighboring nodes in thelocal network of the network node.
 13. The method of claim 12 whereincomputing a gradient of a summed cost function for the network nodecomprises: determining a partial derivative of the summed cost functionwith respect to each of one or more variables in the parameter setting;and computing the gradient of the summed cost function for the networknode as a function of the partial derivatives.
 14. The method of claim12 wherein determining a revised parameter setting for the network nodecomprises: searching the parameter space along the gradient of thesummed cost function to find a scalar that minimizes the summed costfunction; and computing the new parameter setting as a function of thegradient and the scalar.
 15. The method of claim 12 wherein determininga revised parameter setting for the network node further comprisesconstraining the revised parameter setting to be a member of apredetermined set of parameter settings.
 16. A method of determiningparameter settings for a network node in a communication network, themethod comprising: exchanging current parameter settings between thenetwork node and one or more neighboring nodes in a local network of thenetwork node, wherein the network node receives current parametersettings for the neighboring nodes during the exchange; computing, atthe network node, partial derivatives of a local cost function for thenetwork node with respect to each of the neighboring nodes as a functionof the current parameter settings for the network node and theneighboring nodes; exchanging, with the neighboring nodes, the partialderivatives computed by the network node for corresponding partialderivatives with respect of the network node computed based on thecurrent parameter settings by the neighboring nodes; computing agradient of a summed cost function for the network node at a currentparameter setting based on the partial derivatives received from theneighboring nodes; exchanging, with the neighboring nodes, the gradientof the summed cost function for the network node for correspondinggradients of summed cost functions for the neighboring nodes; computing,at the network node, a set of local impact functions for the networknode and the neighboring nodes based on the gradients of the summed costfunctions; exchanging, the local impact functions computed by thenetwork node for corresponding local impact functions computed by theneighboring nodes; determining a summed impact function for the networknode based on the local impact functions for the neighboring nodes and alocal impact function for the network node; determining a revisedparameter setting based on the summed impact function and the gradientof the summed cost function; and sending the revised parameter settingfor the network node to the neighboring nodes in the local network ofthe network node.
 17. The method of claim 16 wherein determining asummed impact function for the network node comprises determining aweighted sum of the local impact functions for the neighboring nodes anda local impact function for the network node.
 18. The method of claim 17wherein determining the revised parameter setting based on the summedimpact function and the gradient of the summed cost function comprises:determining a scalar that minimizes the summed impact function; andcomputing the revised parameter setting for the network node as afunction of the scalar and the gradient of the summed cost function forthe network node.
 19. The method of claim 16 wherein determining arevised parameter setting for the network node further comprisesconstraining the revised parameter setting to be a member of apredetermined set of parameter settings.
 20. A network node in acommunication network, the network node comprising: a communicationinterface for communicating with one or more neighboring nodes in alocal network of the network node; and a configuration processor fordetermining a parameter setting for the network node, the configurationprocessor configured to: receive current parameter settings for theneighboring nodes; compute a gradient of a summed cost function for thenetwork node at a current parameter setting for the network node as afunction of the current parameter settings for the network node and theneighboring nodes; determine a revised parameter setting for the networknode by searching a parameter space along the gradient of the summedcost function; and send the revised parameter setting for the networknode to the neighboring nodes in the local network of the network node.21. The network node of claim 20 wherein the network node is furtherconfigured to: receive a partial derivative with respect to the networknode of a local cost function for each of the neighboring nodes; andcompute the gradient of the summed cost function based on the receivedpartial derivatives for the neighboring nodes.
 22. The network node ofclaim 21 wherein the configuration processor is further configured to:exchange current parameter settings with the neighboring nodes, whereinthe network node receives current parameter settings for its neighboringnodes during the exchange; compute a partial derivative of a local costfunction for the network node based on the current parameter settings ofthe neighboring nodes; and exchange the partial derivatives computed bythe network node with corresponding partial derivatives computed basedon the current parameter settings by the neighboring nodes.
 23. Thenetwork node of claim 20 wherein the configuration processor is furtherconfigured to: receive a local impact function for each of theneighboring nodes, wherein the local impact function for eachneighboring node indicates a contribution of the parameter setting bythe network node on a summed cost function for the neighboring node;determining a summed impact function for the network node based on thelocal impact functions for the neighboring nodes and a local impactfunction for the network node; and determine the revised parametersetting based on the summed impact function and the gradient of thesummed cost function.
 24. The network node of claim 23 wherein theconfiguration processor is further configured to: exchange, with theneighboring nodes, the gradient of the summed cost function for thenetwork node for corresponding gradients of the summed cost functionsfor the neighboring nodes; compute a set of local impact functions forthe network node and the neighboring nodes based on the exchangedgradients of the summed cost functions; and exchange the local impactfunction of the network node for corresponding local impact functionscomputed by the neighboring nodes.
 25. The network node of claim 23wherein the configuration processor is further configured to compute thesummed impact function for the network node as a weighted sum of thelocal impact functions for the neighboring nodes and the local impactfunction for the network node.
 26. The network node of claim 23 whereinthe configuration processor is further configured to: determine a scalarthat minimizes the summed impact function; and compute the revisedparameter setting for the network node as a function of the scalar andthe gradient of the summed cost function for the network node.
 27. Thenetwork node of claim 20 wherein the configuration processor is furtherconfigured to: receive current parameter settings for the neighboringnodes; and determine the summed cost function for the network node basedon the current parameter settings of the neighboring nodes.
 28. Thenetwork node of claim 27 wherein the configuration processor is furtherconfigured to: determine a partial derivative of the summed costfunction with respect to each of one or more variables in the parametersetting; and compute the gradient of the summed cost function for thenetwork node as a function of the partial derivatives.
 29. The networknode of claim 27 wherein the configuration processor is furtherconfigured to: search the parameter space along the gradient of thesummed cost function to find a scalar that minimizes the summed costfunction; and compute the new parameter setting as a function of thegradient and the scalar.
 30. The network node of claim 20 wherein theconfiguration processor is further configured to determine the revisedparameter setting to be a member of a predetermined set of parametersettings.
 31. A network node in a communication network, the networknode comprising: a communication interface for communicating with one ormore neighboring nodes in a local network of the network node; and aconfiguration processor for determining a parameter setting for thenetwork node, the configuration processor configured to: receive currentparameter settings for the neighboring nodes; determine a summed costfunction for the network node based on the current parameter settings ofthe network node and the neighboring nodes; compute a gradient of thesummed cost function at a current parameter setting for the networknode; determine a revised parameter setting for the network node bysearching a parameter space along the gradient of the summed costfunction; and send the revised parameter setting for the network node tothe neighboring nodes in the local network of the network node.
 32. Thenetwork node of claim 31 wherein the configuration processor is furtherconfigured to: determine a partial derivative of the summed costfunction with respect to each of one or more variables in the parametersetting; and compute the gradient of the summed cost function for thenetwork node as a function of the partial derivatives.
 33. The networknode of claim 31 wherein the configuration processor is furtherconfigured to: search the parameter space along the gradient of thesummed cost function to find a scalar that minimizes the summed costfunction; and compute the new parameter setting as a function of thegradient and the scalar.
 34. The network node of claim 31 wherein theconfiguration processor is further configured to constrain the revisedparameter setting to be a member of a predetermined set of parametersettings.
 35. A network node in a communication network, the networknode comprising: a communication interface for communicating with one ormore neighboring nodes in a local network of the network node; aconfiguration processor for determining a parameter setting for thenetwork node, the configuration processor configured to: exchangecurrent parameter settings with the neighboring nodes, wherein thenetwork node receives current parameter settings for the neighboringnodes during the exchange; compute partial derivatives of a local costfunction for the network node with respect to each of the neighboringnodes as a function of the current parameter settings for the networknode and the neighboring nodes; exchange, with the neighboring nodes,the partial derivatives computed by the network node for correspondingpartial derivatives with respect of the network node computed based onthe current parameter settings by the neighboring nodes; compute agradient of a summed cost function for the network node based on thepartial derivatives received from the neighboring nodes; exchange, withthe neighboring nodes, the gradient of the summed cost function for thenetwork node for corresponding gradients of summed cost functions forthe neighboring nodes; compute, at the network node, a set of localimpact functions for the network node and its neighboring nodes based onthe gradients of the summed cost functions; exchange the local impactfunctions computed by the network node for corresponding local impactfunctions computed by the neighboring nodes; determine a summed impactfunction for the network node based on the local impact functions forthe neighboring nodes and a local impact function for the network node;and determine a revised parameter setting based on the summed impactfunction and the gradient of the summed cost function.
 36. The networknode of claim 35 wherein the configuration processor is furtherconfigured to compute the summed impact function as a weighted sum ofthe local impact functions for the neighboring nodes and a local impactfunction for the network node.
 37. The network node of claim 36 whereinthe configuration processor is further configured to: determine a scalarthat minimizes the summed impact function; and compute the revisedparameter setting for the network node as a function of the scalar andthe gradient of the summed cost function for the network node.
 38. Thenetwork node of claim 35 wherein the configuration processor is furtherconfigured to constrain the revised parameter setting to be a member ofa predetermined set of parameter settings.